AWS RDS public access

I am stumped with AWS configuration. My goal is to create a database that's accessible from inside and outside the network.

Here is what I have. RDS instance runs postgresql. Connections from inside the VPC work correctly.

The endpoint is set up to be publicly accessible - and when accessed from the outside, does in fact resolve. However, the connection hangs, indicating the traffic is blocked by somebody.

Security group is good:
Inbound: Port 5432 from 0.0.0.0/0 Outbound: all from 0.0.0.0/0

Subnets. I assume that's where something is wrong, right? At first I had two private and two public subnets in the subnet group. To simplify, I removed the private ones without changing the outcome.

So we have two public subnets:

Both have the same route table with an Internet Gateway

As far as I can tell, everything is in working order... So who is blocking my database connection?